globals [ high-income-cutoff pareto-distribution-alpha pareto-distribution-minimum ] breed [students student] breed [schools school] students-own [target enrolled? income years-in-school school-achievement] schools-own [enrollment achievement traffic-lights-color is-private?] to setup clear-all set-default-shape schools "house" set-default-shape students "person" ask patches [ set pcolor 8 ] set pareto-distribution-alpha 3 set pareto-distribution-minimum 1 set high-income-cutoff (pareto-distribution-minimum / (high-income-percentage / 100) ^ (1 / pareto-distribution-alpha)) create-schools number-of-schools ;default color of schools is yellow ;for discrete choice when the policy implemented, default is 1 ;The procedure paint-school will changes it when necessary [set color yellow set traffic-lights-color 5 fd max-pxcor setxy random-xcor random-ycor set achievement random-normal 5 1 if achievement < 0 [set achievement 0] ifelse (achievement > 6 and random-float 100 < 45.4) [set is-private? TRUE set shape "private-school"][ ifelse (achievement > 4 and random-float 100 < 2.6) [set is-private? TRUE set shape "private-school"] [ ifelse (random-float 100 < 0.4) [set is-private? TRUE][set is-private? FALSE]]] set enrollment 0 set size 1.5 paint-school ] create-students initial-students * 0.9 [ set color gray setxy random-xcor random-ycor set income random-pareto pareto-distribution-alpha pareto-distribution-minimum set enrolled? FALSE set years-in-school random 9 + 1 paint-students ] reset-ticks end to go call-new-students ask students [ choose-school study-a-year seniors-graduate ] ask schools [ enroll ] ask links [ set color white ] tick display-labels end to choose-school ;if school choice is allowed and income is high, students consider achievement when choosing ;agents choose school that maximizes utility ifelse (income > high-income-cutoff and with-school-choice?) [ set target one-of schools with [[income] of myself - (distance myself) * school-transportation-cost / 100 > 0] with-max [(achievement ^ alpha) * (((world-height * sqrt 2) - distance myself) / (world-height * sqrt 2)) ^ (1 - alpha) ] ] [ ifelse (with-school-choice? and traffic-lights?) [ ;if traffic-lights policy is on, low income agents get the color signal and maximize the same utility ;function with discrete values. The policy only works if the agents have school-choice available set target min-one-of schools with [[income] of myself - (distance myself) * school-transportation-cost / 100 > 0 and is-private? = FALSE] with-max [(traffic-lights-color ^ alpha) * (((world-height * sqrt 2) - distance myself) / (world-height * sqrt 2)) ^ (1 - alpha) ] [distance myself] ] [ifelse (with-school-choice?) [set target min-one-of schools with [[income] of myself - (distance myself) * school-transportation-cost / 100 > 0 and is-private? = FALSE] [distance myself] ] ;when failing one of the conditions from above, choose the closest school if affordable [set target min-one-of schools with [[income] of myself - (distance myself) * school-transportation-cost / 100 > 0] [distance myself] ] ]] if target != nobody [create-link-with target set school-achievement [achievement] of target set enrolled? TRUE ] end to call-new-students ;creates new students, which are 10% that of the initial students selected by the user create-students initial-students * 0.1 [ set color gray setxy random-xcor random-ycor set income random-pareto pareto-distribution-alpha pareto-distribution-minimum set enrolled? FALSE set years-in-school 10 paint-students ] end to enroll ;school procedure set enrollment count link-neighbors end to display-labels ask schools [set label round enrollment set label-color black] end to paint-school ask schools [ ifelse achievement > 6 [set color green set traffic-lights-color 6] [if achievement < 4 [set color red set traffic-lights-color 4]] ] end to study-a-year set years-in-school years-in-school - 1 end to paint-students ask students [ ifelse income > high-income-cutoff [set color blue] [if income < high-income-cutoff [set color gray]] ] end to seniors-graduate if years-in-school = 0 [die] end to-report random-pareto [sigma mm] report mm / ( random-float 1 ^ (1 / sigma) ) end ; Cite as: Diego A. Díaz, Ana María Jiménez & Cristián Larroulet (2019) An agent-based model of school choice with information asymmetries, Journal of Simulation, DOI: 10.1080/17477778.2019.1679674 @#$#@#$#@ GRAPHICS-WINDOW 179 10 1048 880 -1 -1 16.91 1 20 1 1 1 0 1 1 1 -25 25 -25 25 1 1 1 ticks 30.0 BUTTON 6 306 91 339 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 93 306 178 339 NIL go T 1 T OBSERVER NIL NIL NIL NIL 0 SLIDER 5 58 175 91 initial-students initial-students 10 10000 3000.0 10 1 NIL HORIZONTAL SLIDER 5 24 175 57 number-of-schools number-of-schools 5 500 100.0 5 1 NIL HORIZONTAL PLOT 1051 10 1511 352 % of students enrolled Year % of students 0.0 10.0 0.0 100.0 true true "" "" PENS "High Achievement" 1.0 0 -14439633 true "" "if (ticks > 0) [plot (sum [enrollment] of schools with [achievement > 6] / count students ) * 100]\n" "Medium Achievement" 1.0 0 -4079321 true "" "if (ticks > 0) [plot (sum [enrollment] of schools with [achievement < 6 and achievement > 4] / count students ) * 100]" "Low Achievement" 1.0 0 -2674135 true "" "if (ticks > 0) [plot (sum [enrollment] of schools with [achievement < 4] / count students ) * 100]" "Unenrolled" 1.0 0 -16777216 true "" "if (ticks > 0) [plot (count students with [enrolled? = FALSE] / count students ) * 100]" BUTTON 94 340 178 374 go one year go NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 5 169 175 202 alpha alpha 0 1 0.05 0.005 1 NIL HORIZONTAL SWITCH 5 203 176 236 with-school-choice? with-school-choice? 0 1 -1000 PLOT 1051 358 1511 571 Average Achievement of Students Year Achievement 0.0 10.0 -1.0 1.0 true true "" "" PENS "All students" 1.0 0 -4079321 true "" "if (ticks > 0) [\nplot sum [school-achievement] of students with [enrolled?]\n/ count students with [enrolled?] - 5 \n]" "High-income" 1.0 0 -13345367 true "" "if (ticks > 0) [\nplot sum [school-achievement] of students with [income > high-income-cutoff and enrolled?]\n/ count students with [income > high-income-cutoff and enrolled?] - 5 \n]" "Low-income" 1.0 0 -4539718 true "" "if (ticks > 0) [\nplot sum [school-achievement] of students with [income < high-income-cutoff and enrolled?]\n/ count students with [income < high-income-cutoff and enrolled?] - 5 \n]" SWITCH 5 237 176 270 traffic-lights? traffic-lights? 1 1 -1000 PLOT 1517 11 1752 161 Income distribution of students Income Students 1.0 6.0 0.0 100.0 true false "set-plot-x-range 1 6\nset-plot-y-range 0 50\nset-histogram-num-bars 20" "" PENS "default" 1.0 1 -16777216 true "" "histogram [income] of students\n;; draws a histogram showing how many turtles there are\n;; of each color" PLOT 1518 165 1751 339 Achievement distribution of schools Achievement Number of schools -3.0 3.0 0.0 20.0 true false "set-histogram-num-bars 10" "" PENS "School achievement" 1.0 1 -16777216 true "" "histogram [achievement - 5] of schools\n;; draws a histogram showing how many turtles there are\n;; of each color" SLIDER 6 94 175 127 high-income-percentage high-income-percentage 1 100 21.0 1 1 NIL HORIZONTAL SLIDER 6 271 176 304 school-transportation-cost school-transportation-cost 0 100 30.0 1 1 NIL HORIZONTAL TEXTBOX 9 132 159 160 The next parameters can be changed while ticking: 11 0.0 1 @#$#@#$#@ ## WHAT IS IT? This model implements a school selection model that allows to study the effects of school choice and a policy implemented in Chile in 2010 known as traffic lights, in which a discrete signal of school achievement was given to families so they would make a better decision. It is submitted as supplemental material with the paper: An agent-based model of school choice with information asymmetries, submitted to the Journal of Simulation. ## HOW IT WORKS There are two types of agents, schools and students. Both are placed randomly in the world. Both do not move. Students have an income level drawn from a normal distribution and they must choose a school, which is represented visually as a link to the school. They stay for a total of 10 years in school and then they graduate (or die in the model). Every year new students are created and appear in random places in the world. Schools have an achievemnt level drawn from a normal distribution. Students have an income level drawn from a Pareto distribution. As in Chile, a small percentage of schools can be private when school choice is allowed, in which case they may charge tuition, making them accesible only to high income students. The percentage of high income students is selected by the user. The important mechanic is the school selection process, which is implemented in procedure choose-school. Without school choice, every student is assigned a school in their neighborhood, which is the school closest to them. With school choice, students with a high income level will choose acoording to a utility function that considers both achievement and proximity the school. Low income students still select the closest option, either because they don´t know the achievement of schools or because they don´t care. Attending public schools also has a cost, which is a transportation cost that agents may be able to afford depending on their income. With traffic-lights? on, low income students know the signal of achievement of schools provided by the government, represented by the color of the school. Assuming they care about achievement, since the signal can only have 3 values, their choice still won't be as optimal as high-income students. ## HOW TO CITE If you mention this model or the NetLogo software in a publication, we ask that you include the citations below. For the model itself: Diego A. Díaz, Ana María Jiménez & Cristián Larroulet (2019) An agent-based model of school choice with information asymmetries, Journal of Simulation, DOI: 10.1080/17477778.2019.1679674 Please cite the NetLogo software as: Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. ## QUESTIONS AND COMMENTS Please address the developer and corresponding author of the publication, Diego A. Díaz at: diegodiaz@uchicago.edu @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 90 90 120 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle -7500403 true true 177 132 38 Circle -7500403 true true 70 85 38 Circle -7500403 true true 130 25 38 Circle -7500403 true true 96 51 108 Circle -16777216 true false 113 68 74 Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218 Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 private-school false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 Polygon -7500403 true true 15 120 150 15 150 15 30 120 135 60 90 60 Polygon -16777216 true false 15 120 150 15 285 120 15 120 90 60 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 6.0.4 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ setup go (sum [enrollment] of schools with [achievement > 6] / count students ) * 100 @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 0 @#$#@#$#@